1 Executive Summary

1.1 Revenue Analysis

As the “Resource Availability Rate” decreases, total revenue also declines at an increasing amount (additional 830 million - 1200 million for every 10% reduction in resource availability)
On average, revenue decreases by an additional 4% for each 10% drop in resource availability.
When resource availability falls to 60%, revenue is 70% compared to one under full resource availability condition.
This pattern is consistently observed at regional level

Statistical analysis of the solution set for each resource availability rate reveals greater variation in outcomes under more severe resource shortage scenarios. (Definition: a solution set is the set of solution that contains all pairs of e1 and e2)
This behavior in total revenue suggests the model’s increased sensitivity to “equitable” constraints (e1, e2) when resources are limited. Specifically, under conditions of limited resource availability, the “default” gap in treatment opportunities among and within cluster is higher, which lead to a more diverse set of outcome when e1 and e2 are reduced. From OR standpoint, equitable constraints are more likely to become model’s binding constraints when the resource availability is low.

the lower fulfillment, more sensitive with equity constraint (binding) –> also relvevant to revenue

A deeper analysis on treatment opportunity confirmed the hypothesis in revenue analysis about model sensitivity to equitable constraints. Additionally, the resource shortage condition has stronger effect on cluster 1 and cluster 2 as these are cluster with lower revenue per resource consumed. In specific, under limited resource and revenue maximization goal, the model will prioritize to maintain high treatment opportunity for higher-revenue clusters (cluster 3 - cluster 6) and allocate remaining resource to lower-revenue clusters (cluster 1 and cluster 2). While the resource amount allocated to higher-revenue clusters remains stable, the variation in resource capacity will directly lead to the variation in the amount of “remaining resource” available for lower-revenue clusters, then the treatment opportunity for these clusters.
According to the figure, the variation in the outcome of lower-revenue clusters starts appearing at resource availability rate = 0.85 while the variation in the outcome of higher-revenue ones happens from resource availability rate = 0.75 - where the resources for lower-revenue cannot significantly reduce further, due to the equitable constraints among clusters.

This analysis brings new perspectives on equitable healthcare implementation. The figure illustrates the cumulative revenue loss attributed to reduced resource availability and the impact of target inequity among clusters. Generally, a lower resource availability rate and lower e1 correlates with a sharper revenue decline, which is depicted as a darker blue triangle in the upper portion of the heat map. Beyond the findings from previous analyses regarding the relationship between revenue and the e1 constraint, this section highlights that within the same e1 value, revenue loss is higher as resource shortages become more severe. In case-mix planning, for the same e1, hospital can consider investing for capacity expansion and accept lower revenue loss. Though opportunity cost paid for equitable healthcare access in this case does not reduce compared to the situation where hospital accept the whole revenue loss without making investment, the hospital and society can yield higher gain through greater revenue and higher treatment opportunity.
Furthermore, this analytical approach, when combined with the costs of healthcare infrastructure, can lay the groundwork for a comprehensive cost-benefit analysis on capacity expansion to promote equitable healthcare access

A similar pattern can be seen in analysis within clusters.
# Treatment Opportunity Analysis ## Among Clusters

This analysis provides a deeper perspective on the insights presented in the “Treatment Opportunity Analysis” section of the Executive Summary. When target inequity among clusters is high (e1 > 0.6), the reduction in resource availability significantly impacts lower-revenue clusters. Conversely, at lower levels of e1, where the treatment opportunity gap among clusters is more constrained, the burden of resource shortages is distributed more evenly, affecting higher-revenue clusters as well.

The figure illustrates the evolution of treatment opportunity gaps between classes within clusters under various resource availability scenarios. The chart reveals significant within-cluster gaps in both Cluster 1 and Cluster 2. Specifically, Cluster 1 exhibits the largest treatment opportunity gap when the resource availability rate is ≥ 0.8, whereas Cluster 2 takes the lead in this gap when the resource availability rate drops to ≤ 0.7.

This figure aims to explore further the aforementioned pattern.
For resource availability rates of ≥ 0.8, where there is sufficient capacity to maintain high treatment opportunities in Clusters 2 through 6, the primary dynamics occur in Cluster 1, the most disadvantaged cluster. Within Cluster 1, limited resources are prioritized to meet the demand from DRGs with Above-Fitted-Value Revenue, resulting in a significant within-cluster gap. As the resource availability rate decreases further, this within-cluster gap narrows because the treatment opportunities for most DRGs in this cluster have already become very low.
When the resource availability rate drops to ≤ 0.7, the model is constrained by the need to maintain target treatment equity among clusters, preventing a significant reduction in Cluster 1’s treatment opportunity. As a result, the second most disadvantaged cluster, Cluster 2, begins to be affected. The same principles apply here: under limited resource conditions, the model prioritizes maintaining high treatment opportunities for DRGs with Above-Fitted-Value Revenue, leaving minimal resources for others, which increases the gap in treatment opportunities between these two classes.